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Math Help - quadratic forms

  1. #1
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    quadratic forms

    Consider a quadratic form f(x,y) = ax^2 + bxy + cy^2 with a,b,c \in \mathbb{Z} and discriminant D = b^2 - 4ac

    We know that f factors as a product of linear forms (ux+vy)(u'x+v'y) with rational coefficients if and only if D is a square.
    Under which conditions for a,b,c are u,v,u',v' \in \mathbb{Z}?
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    You might want to use Gauss's Lemma.
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  3. #3
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    I don't get Gauss lemma and I don't see how to use it here.
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